nonabelian tensor
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Author(s):  
F. Fasihi ◽  
S. Hadi Jafari

Let [Formula: see text] be a group given by a free presentation [Formula: see text]. The 2-nilpotent multiplier of [Formula: see text] is the abelian group [Formula: see text] which is invariant of [Formula: see text] [R. Baer, Representations of groups as quotient groups, I, II, and III, Trans. Amer. Math. Soc. 58 (1945) 295–419]. An effective approach to compute the 2-nilpotent multiplier of groups has been proposed by Burns and Ellis [On the nilpotent multipliers of a group, Math. Z. 226 (1997) 405–428], which is based on the nonabelian tensor product. We use this method to determine the explicit structure of [Formula: see text], when [Formula: see text] is a finite (generalized) extra special [Formula: see text]-group. Moreover, the descriptions of the triple tensor product [Formula: see text], and the triple exterior product [Formula: see text] are given.



Author(s):  
O. Kalteh ◽  
S. Hadi Jafari

AbstractIn this paper, we describe the explicit structures of nonabelian tensor squares of nonabelian groups of order $$p^3q$$ p 3 q , where p and q are distinct prime numbers and $$p>2$$ p > 2 . Our method is based on determining the structures of their Schur multipliers by applying some well-known results and the presentations of groups, which leads us to obtain the orders of their nonabelian tensor squares.



Author(s):  
Graham Ellis

This chapter introduces some of the basic ingredients of cohomological group theory and describes datatypes and algorithms for implementing them on a computer. These are illustrated using computer examples involving: explicit cocycles, classification of abelian and nonabelian group extensions, crossed modules, crossed extensions, five-term exact sequences, Hopf’s formula, Bogomolov multipliers, relative central extensions, nonabelian tensor products of groups, and cocyclic Hadamard matrices.



A Bieberbach set can be categorized as a torsion free crystallographic set. Some properties can be explored from the set such as the property of nonabelian tensor square. The nonabelian tensor square is one type of the homological factors of sets. This paper focused on a Bieberbach set with C2 ×C2 as the point set of lowest dimension three. The purpose of this paper is to determine the generalization of the formula of the nonabelian tensor square of one Bieberbach set with point set C2 × C2of lowest dimension three which is denoted by S2 (3) up to dimensionn. The polycyclic presentation, the abelianization of S2 (3) and the central subgroup of the nonabelian tensor square of S2 (3) are also presented.



2018 ◽  
Vol 7 (4.1) ◽  
pp. 9
Author(s):  
S Rashid ◽  
. .

In this paper, the software package Groups, Algorithms and Programming (GAP)   is used to verify the hand calculation of  the nonabelian tensor square for groups of order 8q, where q is an odd prime. 



2018 ◽  
Vol 80 (5) ◽  
Author(s):  
Mohammed Khalid Shahoodh ◽  
Mohd Sham Mohamad ◽  
Yuhani Yusof ◽  
Sahimel Azwal Sulaiman

The compatible actions played an important role before determining the nonabelian tensor product of groups. Different compatible pair of actions gives a different nonabelian tensor product even for the same group. The aim of this paper is to determine the exact number of the compatible pair of actions for the finite cyclic groups of p-power order where p is an odd prime. By using the necessary and sufficient number theoretical conditions for a pair of the actions to be compatible with the actions that have p-power order, the exact number of the compatible pair of actions for the finite cyclic groups of p-power order has been determined and given as a main result in this paper.   



2017 ◽  
Vol 13 (4) ◽  
pp. 788-791
Author(s):  
Siti Afiqah Mohammad ◽  
Nor Haniza Sarmin ◽  
Hazzirah Izzati Mat Hassim

Exploration of a group's properties is vital for better understanding about the group.  Amongst other properties, the homological invariants including the nonabelian tensor square of a group can be explicated by showing that the group is polycyclic.  In this paper, the polycyclic presentations of certain crystallographic groups with quaternion point group of order eight are shown to be consistent; which implies that these groups are polycyclic.



2017 ◽  
Vol 79 (7) ◽  
Author(s):  
Nor Fadzilah Abdul Ladi ◽  
Rohaidah Masri ◽  
Nor'ashiqin Mohd Idrus ◽  
Nor Haniza Sarmin ◽  
Tan Yee Ting

Bieberbach groups are torsion free crystallographic groups. In this paper, our focus is on the Bieberbach groups with elementary abelian 2-group point group,  The central subgroup of the nonabelian tensor square of a group  is generated by  for all  in  The purpose of this paper is to compute the central subgroups of the nonabelian tensor squares of two Bieberbach groups with elementary abelian 2-point group of dimension three. 



2017 ◽  
Vol 893 ◽  
pp. 012006
Author(s):  
Siti Afiqah Mohammad ◽  
Nor Haniza Sarmin ◽  
Hazzirah Izzati Mat Hassim


2017 ◽  
Vol 42 (4) ◽  
pp. 1295-1304
Author(s):  
Peyman Niroomand ◽  
Farangis Johari ◽  
Mohsen Parvizi ◽  
Francesco G. Russo


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